Behind the neo-gothic scenery at the supreme court, there is a tradition that after every hearing the most junior justice on the panel addresses the others first – allowing him or her to give an unprejudiced assessment of the issues.

The idea that one of the country's sharpest legal minds, informed by more than 30 years of courtroom experience, could be swayed by elders is an example of the hierarchic rituals and refined working practices operating among those who sit on the highest bench in the land.

The 12 "justices" – as the judges prefer to be known – disentangle points of mind-wrenching complexity from contradictory precedents, interpret broad principles enshrined in human rights legislation, influence the development of the law and, as privy councillors, deliberate on the death penalty in foreign jurisdictions.

Demystifying its hidden decision-making process has been one of the court's aims, though as Lady Hale, the only female justice, cautioned: "It's a very narrow dividing line between improving public understanding … and diminishing the dignity and respect the court should have. We are not politicians."

In the soft-carpeted upper corridors of the court, where private rooms overlook Parliament Square, five justices – Lord Phillips, the president of the court; Lord Hope, the deputy president; Lady Hale; Lord Mance; and Lord Dyson – explained to the Guardian how the machinery of justice delivered judgments of national significance.

Dyson, 68, was appointed 18 months ago and described the peculiar order of procedure. "Usually straight after the hearing," he said, the justices on the panel would assemble and "set out in summary, maybe for five minutes or so, his or her view on the issue of the case".

The review always starts with the newest appointee. "The rationale is that the junior member of the court, it is thought, may be swayed unduly by hearing the senior members first.

"I think that's to underestimate the backbone of the junior members of the court, but that is the tradition. For the last 18 months I've tended to bat first on these occasions … Sometimes we are at disagreement, sometimes at one."

The intensity of the legal reasoning affects justices in different ways. Asked if cases kept him awake at night, Phillips said: "Very often, surprisingly. Not because of anxiety, but because when your mind is working vigorously, after you have had a few hours' sleep, it sometimes wakes you up to continue with the internal debate."

Hope, formerly a judge in Scotland, admitted to doing much of his thinking on public transport. "I tend to work these ideas out during my travels," he explained. "I travel quite a bit as I go back to Scotland every weekend and it's a therapy being on the underground or in the aeroplane or on the train or whatever it is with time to think, so things work themselves through without having to trouble my sleep."

Changing one's mind as ideas develop is a common experience. "We all do," Hale said. "By definition the cases that come to us are not likely to have a straightforward answer." For Dyson, the act of writing crystallises decisions. "Sometimes my final conclusions don't emerge until I have actually written the judgment," he explained.

Legal commentators have attempted to characterise justices as being divided between liberals and conservatives, following the pattern of the US supreme court, or, alternatively, between those who consistently support the individual against the state – and vice versa.

The justices themselves believe they are less predictable. In one recent case involving a particularly convoluted statute, Phillips said: "Seven of us sat … we produced initially four different answers … each one different from the court of appeal and also the court at first instance. That's an example of just how difficult a case can be." On rare occasions, he conceded, individual justices could be identified as being "more conservative" or "more liberal".

Given such variety of opinions, the question arises as to whether the majesty of the state's highest court might – if a judicial panel had been differently composed – have arrived at an entirely contradictory conclusion.

The choice of who sits on which case depends on ensuring that the bench's expert in any legal field – such as intellectual property or company law – hears those relevant cases. "Once that is done then the selection is really random," Phillips added.

There is no disgrace, Hope said, in being in a minority and returning a dissenting judgment: "There's no feeling of animosity. Sometimes [opinions] are fairly strongly expressed but they are nothing like … some of the remarks you see in the US supreme court that judges make about each other's decisions, usually in footnotes. But they can be very trenchant."

Occasionally justices find themselves surprised by colleagues' conclusions. "They may come up with something that hasn't really been flagged up in the arguments and then it's more difficult to understand why they have reached the conclusion they have," Hale said. "But we all have to explain ourselves."

This month Phillips, 73, a former lord chief justice, said he would retire in the summer of 2012. His departure will trigger a succession race. Among those mentioned has been Lord Neuberger, the current master of the rolls, who is head of the civil judiciary.

In future, justices will have to step down at 70, rather than 75. Decades of sleuthing through legal textbooks have imbued Phillips with the expression of a bloodhound. Asked what he would miss most, he replied: "The companionship of my fellow justices."

The court is currently one down on its full complement of 12 justices since the death of Lord Rodger in June. Two new posts, one to replace Lord Brown, who retires next spring, have been advertised, each at a salary of £206,857.

Sumption, author of scholarly medieval histories, is due to deliver a lecture next month under the title of Judicial and Political Decision Making: The Uncertain Boundary. That headline did not unsettle Phillips. "There's always a bit of a grey area between the province of the courts and the province of parliament," he said.

Among the means by which the supreme court has emphasised its independence is its choice of decoration for the grandiose former civic centre, described by one historian as a celebration of art nouveau gothic.

Portraits of past judges look down on modern inscriptions. "Justice cannot be for one side but must be for both," says a motto on a glass screen at the rear of one of its three courtrooms.

Pop art carpets designed by Sir Peter Blake incorporate a motif of roses, thistles, leeks and blue flax flowers symbolising the jurisdictions of England, Scotland, Wales and Northern Ireland. Not all the justices are enamoured of the design.

There is a public cafe in the basement, close to what were once the lock-up cells for Middlesex crown court. Justices have their own private dining room and the use of a three-storey library beneath a vaulted ceiling. The oldest legal volume dates back to the 1660s. A glass balustrade is engraved with mottos chosen by the first 12 justices, including quotations by Disraeli – "Justice is truth in action", Martin Luther King – "Injustice anywhere is injustice everywhere", Aristotle and Tolstoy.

The number of judicial assistants, selected from among high-flying young lawyers, has doubled since the court left the House of Lords, providing more legal support. All eight assistants spend a week gaining experience at the US supreme court.

One of the justices' duties is to sit in judgment on death penalty appeals from Caribbean countries that have retained the UK's privy council as their ultimate chamber of appeal. Asked how he felt about capital punishment cases, Dyson said: "Extremely uncomfortable. I'm not aware of any case in recent years in which the death penalty sentence has been upheld … the jurisprudence propounded by the privy council has been such as to make it extremely difficult to make lawful a death penalty sentence."

Hope agreed: "They are very anxious cases. [But] we have to serve the jurisdiction that comes to us, so it's not our position to argue with the death penalty as such." The court has removed the mandatory death penalty, he pointed out, "which is the most objectionable".

The supreme court has led the way in televising its proceedings. None of the justices were worried about the presence of cameras in court but all acknowledged the impact on lower courts – where there are witnesses and defendants – would be different.

"It is an almost invisible exercise as far as we're concerned," Mance said. "I don't notice the cameras, I don't notice that I'm being filmed and I don't think it has any effect on judges' behaviour."

Hale added: "We are too busy concentrating on the job in hand … If it was a trial where there were witnesses having to give evidence for the very first time, not regularly in court, there might be quite serious problems of whether their evidence would be affected."

How do they feel about politicians attacking their judgments? "I remember years ago making decisions which Michael Howard [the former Conservative home secretary] … didn't like at all and he criticised the judiciary fiercely and I thought unfairly," Dyson said. "But I couldn't answer back."

Phillips concurred. "To say we would love to be able to respond is probably overstating it. It's just it's an incident of our life that we don't and can't respond. It would be disastrous if we tried.

"You have to let your judgments speak for themselves … Sometimes you would like to make yourself heard but you have to resist the temptation."